Table 2.

Estimated parameters of marginal AR(1)-GJR-GARCH(1,1) models with a normal or Student’s $t$ innovation.

		$\phi$	$\psi$	$\xi$	$\omega$	$\eta$	$\beta$	$\gamma$	$\nu$	$\eta +\beta +\frac{1}{2}\gamma$	LL	AIC	LR
Before COVID-19
OIL	$N$	0.025	−0.004		0.137**	0.013	0.908***	0.083**		0.962	−1105.683	2223.366	45.328***
		(0.078)	(0.047)		(0.068)	(0.021)	(0.033)	(0.033)
	$t$	0.072	−0.010		0.121*	0.011	0.917***	0.076**	6.257***	0.966	−1094.996	2203.992	26.126***
		(0.074)	(0.044)		(0.066)	(0.025)	(0.031)	(0.037)	(1.769)
BTC	$N$	−0.104	0.074		1.307**	0.089**	0.852***	0.003		0.942	−1588.363	3188.726	77.108***
		(0.200)	(0.049)		(0.621)	(0.040)	(0.059)	(0.031)
	$t$	−0.008	0.028		0.143	0.095***	0.901***	0.004	3.190***	0.999	−1520.213	3054.426	84.939***
		(0.118)	(0.038)		(0.193)	(0.028)	(0.026)	(0.035)	(0.326)
USDT	$N$	−0.004	−0.414***		0.017***	0.278***	0.680***	0.059		0.988	−337.770	687.541	269.089***
		(0.011)	(0.048)		(0.006)	(0.102)	(0.074)	(0.104)
	$t$	−0.012	−0.368***		0.028***	0.281**	0.580***	0.244	4.013***	0.983	−293.861	601.721	107.295***
		(0.010)	(0.042)		(0.010)	(0.114)	(0.091)	(0.181)	(0.683)
USD	$N$	0.000	−0.029		0.000	0.003	0.988***	0.016		0.999	−160.254	332.509	18.751***
		(0.013)	(0.043)		(0.000)	(0.006)	(0.001)	(0.012)
	$t$	0.001	−0.029		0.000	0.003	0.988***	0.016	62.458	0.999	−160.183	334.366	17.886***
		(0.013)	(0.043)		(0.000)	(0.006)	(0.001)	(0.012)	(144.279)
During COVID-19
OIL	$N$	0.167*	0.024	0.001	0.339***	0.097***	0.797***	0.188***		0.988	−1606.069	3226.138	703.530***
		(0.095)	(0.048)	(0.003)	(0.101)	(0.032)	(0.025)	(0.058)
	$t$	0.300***	−0.008	0.004	0.361***	0.106**	0.807***	0.125*	4.003***	0.976	−1555.447	3126.894	171.194***
		(0.079)	(0.041)	(0.003)	(0.127)	(0.052)	(0.033)	(0.069)	(0.629)
BTC	$N$	0.188	−0.016	0.001	5.788**	0.000	0.665***	0.187**		0.759	−1930.915	3875.830	30.297***
		(0.182)	(0.052)	(0.005)	(2.324)	(0.061)	(0.094)	(0.091)
	$t$	0.255**	−0.065**	0.003	0.450	0.085**	0.941***	−0.056*	3.004***	0.998	−1850.745	3717.490	19.234***
		(0.128)	(0.032)	(0.004)	(0.342)	(0.036)	(0.019)	(0.034)	(0.389)
USDT	$N$	0.002	−0.242***	0.000**	0.000***	0.318***	0.829***	−0.296***		0.999	432.076	−850.152	1394.280***
		(0.002)	(0.045)	(0.000)	(0.000)	(0.008)	(0.012)	(0.010)
	$t$	0.000	−0.368***	−0.000	0.000***	0.356***	0.687***	−0.088	3.856***	0.999	742.415	−1468.830	588.191***
		(0.001)	(0.038)	(0.000)	(0.000)	(0.069)	(0.048)	(0.104)	(0.373)
USD	$N$	0.010	0.028	0.000	0.011**	0.105***	0.828***	−0.001		0.933	−303.450	620.900	85.734***
		(0.015)	(0.042)	(0.000)	(0.005)	(0.034)	(0.049)	(0.042)
	$t$	0.010	0.027	0.000	0.011**	0.106***	0.828***	−0.002	78.507	0.933	−303.421	622.842	62.051***
		(0.015)	(0.042)	(0.000)	(0.005)	(0.035)	(0.050)	(0.042)	(195.995)

Note: LL and AIC refer to the maximized conditional log-likelihood and the corresponding Akaike information criterion, respectively. Meanwhile, LR is the likelihood ratio test statistic utilized to test the null hypothesis of homoscedasticity, i.e., H${}_0$: $\eta =\beta =\gamma =0$, as in Hoang and Baur (2021). This statistic is asymptotically chi-square distributed with three degrees of freedom. Each number in parentheses is the standard error of the estimated parameter. The asterisks *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.